Assuming Newton's gravity and GR to be valid at all scales, leads to the dark
matter hypothesis as a forced requirement demanded by the observed dynamics and
measured baryonic content at galactic and extragalactic scales. Alternatively,
one can propose a contrasting scenario where gravity exhibits a change of
regime at acceleration scales a<a0, and obtain just as good a fit to
observations across astrophysical scales. This modified regime at a<a0 will
generically be characterised by equilibrium velocities which become independent
of distance, regardless of the details of the modified gravity theory in
question. Here we identify a critical experiment in this debate offered by wide
orbit binary stars. Since for 1 M0 systems the acceleration drops below a0 at
scales of around 7000 AU, an statistical survey of wide binaries with relative
velocities and separations reaching beyond 10^4 AU should yield a conclusive
answer to the above debate. We perform such a study using first a recent
catalogue of wide binaries from the {\it Hipparcos} satellite having high
signal to noise relative velocity measurements. The experiment is repeated
using a more extensive low signal to noise wide binary catalogue from the
ground based Sloan Digital Sky Survey. Results from both samples are
compatible, showing clearly an upper limit to the relative velocities in wide
binaries which is independent of separation for over three orders of magnitude,
in analogy with galactic flat rotation curves in the same a<a0 acceleration
regime. Our results are strongly suggestive of a breakdown of Kepler's third
law precisely below a0 scales, precisely as predicted by modified gravity
theories designed not to require any dark matter at galactic scales and beyond.

The authors claim to have detected an upper limit to the relative velocities in wide binary star systems, independent of separation for over three orders of magnitude, as predicted by modified gravity theories.

I'd be interested in opinions on that. Stars are not a usual cosmologist's specialty, so I can't really judge. I wonder, provided these measurements are correct, if one can still try to save dark matter as the factor responsible for this phenomenon.